Randomized trial investigates multiple new solutions in fractional Schrödinger equations, suggesting significant implications for theoretical physics.
This paper establishes a new dichotomy phenomenon concerning concentrating solutions for the following perturbed fractional Schrödinger equation: where and is a potential function on . By means of Lyapunov–Schmidt reduction, we establish the existence of multiple new solutions whose peaks simultaneously concentrate in bounded domains and near infinity, thereby fully characterizing the concentration–compactness profile.
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Deng et al. (2026) studied this question.
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